Finite Group Databasebeta

← #14326778

Subgroups — #14326778

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91761C211yesmaximal, characteristic
2C3×C5×#382C211yesmaximal, characteristic, complemented
3#11751091C212yesmaximal
4#11751077C212yesmaximal, complemented
5#11751033C211yesmaximal, characteristic, complemented
6#11750770C212yesmaximal
7#11750768C211yesmaximal, characteristic
8#11750767C211yesmaximal, characteristic
9#11750751C211yesmaximal, characteristic, complemented
10#11750750C212yesmaximal, complemented
11#11750749C211yesmaximal, characteristic, complemented
12#10605887—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2212yes—
15C2×C3×C42×C5C2211yescharacteristic
16C2×#6714C2212yes—
17C2×#6714C2212yes—
18C2×#6714C2211yescharacteristic
19C2×#6714C2211yescharacteristic
20C2×#6712C2212yes—
21C2×#6712C2212yes—
22C2×#6712C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C4×Dic15C2212yes—
25C2×C4×Dic15C2212yes—
26C2×C4×Dic15C2212yes—
27C2×C4×Dic15C2211yescharacteristic
28#91761C418yescomplemented
29C3×C5×#95C2211yescharacteristic
30C3×C5×#95C2212yes—
31C3×C5×#95C2211yescharacteristic
32#91115C2211yescharacteristic
33#91115C2212yes—
34#91115C2212yes—
35#91115C2211yescharacteristic
36#91115C2212yes—
37#74156—51nomaximal, Hall
38C2×#4018—31no—
39C5×#382D311yescharacteristic, complemented
40#65279—32no—
41#65261—32no—
42#65221—31no—
43#64958—32no—
44#64956—31no—
45#64955—31no—
46#64939—31no—
47#64938—32no—
48#64937—31no—
49C23×D15C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×Dic15C2311yescharacteristic
60C2×C4×D15—24no—
61C2×C4×D15C2×C414yes—
62C3×C5×C4⋊C4—42no—
63C3×C42×C5C2×C414yes—
64#6714—24no—
65#6714—42no—
66#6714C2×C414yes—
67#6714C2×C414yes—
68#6712—24no—
69#6712—42no—
70#6712C2×C414yes—
71#6712C2×C414yes—
72C4×Dic15—24no—
73C4×Dic15—24no—
74C4×Dic15—24no—
75C4×Dic15C2×C414yes—
76C2×#872—51no—
77C3×#382D511yescharacteristic, complemented
78#4990—52no—
79#4976—52no—
80#4932—51no—
81#4669—52no—
82#4667—51no—
83#4666—51no—
84#4650—51no—
85#4649—52no—
86#4648—51no—
87C22×C4×D5—31no—
88C2×C5×C4⋊C4C2×D312yes—
89C2×C42×C5C2×D311yescharacteristic
90C2×#685—31no—
91C2×#685—31no—
92C2×#685—32no—
93C2×#685—32no—
94C2×#683—31no—
95C2×#683—31no—
96C2×#683—32no—
97C2×#683—32no—
98C2×C4×Dic5—31no—
99C2×C4×Dic5—32no—
100C2×C4×Dic5—32no—
101C2×C4×Dic5—32no—
102#4018—38no—
103C5×#95C2×D311yescharacteristic
104C5×#95C2×D312yes—
105C5×#95C2×D311yescharacteristic
106#3963—31no—
107#3963—32no—
108#3963—32no—
109#3963—31no—
110#3963—32no—
111#2346—151noSylow
112C23×C3×C5C2411yescharacteristic
113C22×D15—22no—
114C22×D15—22no—
115C22×D15—21no—
116C22×D15—21no—
117C22×D15C22×C412yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C22×C412yes—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5C22×C412yes—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15C22×C412yes—
140C2×Dic15C22×C412yes—
141C2×Dic15C22×C412yes—
142C2×Dic15#4114yes—
143C2×Dic15#4114yes—
144C4×D15—28no—
145C22×C4×D3—51no—
146C2×C3×C4⋊C4C2×D512yes—
147C2×C3×C42C2×D511yescharacteristic
148C2×(C2×D3)⋊C4—51no—
149C2×(C2×D3)⋊C4—51no—
150C2×(C2×D3)⋊C4—52no—
151C2×(C2×D3)⋊C4—52no—
152C2×Dic3⋊C4—51no—
153C2×Dic3⋊C4—51no—
154C2×Dic3⋊C4—52no—
155C2×Dic3⋊C4—52no—
156C2×C4×Dic3—51no—
157C2×C4×Dic3—52no—
158C2×C4×Dic3—52no—
159C2×C4×Dic3—52no—
160#872—58no—
161C3×#95C2×D511yescharacteristic
162C3×#95C2×D512yes—
163C3×#95C2×D511yescharacteristic
164C3⋊#95—51no—
165C3⋊#95—52no—
166C3⋊#95—52no—
167C3⋊#95—51no—
168C3⋊#95—52no—
169C23×D5—31no—
170C22×C4×C5C22×D312yes—
171C22×C4×C5C22×D312yes—
172C22×C4×C5C22×D311yescharacteristic
173C22×C4×C5C22×D311yescharacteristic
174C22×C4×C5C22×D311yescharacteristic
175C22×Dic5—31no—
176C22×Dic5—32no—
177C22×Dic5—31no—
178C22×Dic5—31no—
179C22×Dic5—32no—
180C2×C4×D5—34no—
181C2×C4×D5—64no—
182C5×C4⋊C4—42no—
183C42×C5C4×D314yes—
184#685—34no—
185#685—34no—
186#685—64no—
187#685—122no—
188#683—34no—
189#683—34no—
190#683—64no—
191#683—122no—
192C4×Dic5—34no—
193C4×Dic5—64no—
194C4×Dic5—64no—
195C4×Dic5—64no—
196C2×#117—151no—
197#389—152no—
198#388—152no—
199#388—152no—
200#382—151no—
201#382D1511yescharacteristic, complemented
202#380—151no—
203C4×C4⋊C4—152no—
204C4×C22⋊C4—151no—
205#376—151no—
206#376—151no—
207C22×C3×C5C23×C411yescharacteristic
208C22×C3×C5C2×#4112yes—
209C22×C3×C5C2×#4112yes—
210C22×C3×C5H(5,𝔽2)11yescharacteristic
211C22×C3×C52−1+411yescharacteristic
212C2×D15—22no—
213C2×D15—22no—
214C2×D15—22no—
215C2×D15—42no—
216C2×D15—42no—
217C3×C4×C5—22no—
218C3×C4×C5—22no—
219C3×C4×C5—22no—
220C3×C4×C5—42no—
221C3×C4×C5—42no—
222Dic15—22no—
223Dic15—22no—
224Dic15—24no—
225Dic15—42no—
226Dic15#11714yes—
227C23×D3—51no—
228C22×C3×C4C22×D512yes—
229C22×C3×C4C22×D512yes—
230C22×C3×C4C22×D511yescharacteristic
231C22×C3×C4C22×D511yescharacteristic
232C22×C3×C4C22×D511yescharacteristic
233C22×Dic3—51no—
234C22×Dic3—52no—
235C22×Dic3—51no—
236C22×Dic3—51no—
237C22×Dic3—52no—
238C2×C4×D3—54no—
239C2×C4×D3—104no—
240C3×C4⋊C4—42no—
241C3×C42C4×D514yes—
242(C2×D3)⋊C4—54no—
243(C2×D3)⋊C4—54no—
244(C2×D3)⋊C4—104no—
245(C2×D3)⋊C4—202no—
246Dic3⋊C4—54no—
247Dic3⋊C4—54no—
248Dic3⋊C4—104no—
249Dic3⋊C4—202no—
250C4×Dic3—54no—
251C4×Dic3—104no—
252C4×Dic3—104no—
253C4×Dic3—104no—
254C23×C5C23×D311yescharacteristic
255C22×D5—32no—
256C22×D5—61no—
257C22×D5—61no—
258C22×D5—62no—
259C22×D5—62no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5C2×C4×D312yes—
271C2×C4×C5C2×C4×D312yes—
272C2×C4×C5C2×C4×D312yes—
273C2×Dic5—32no—
274C2×Dic5—34no—
275C2×Dic5—32no—
276C2×Dic5—32no—
277C2×Dic5—34no—
278C2×Dic5—61no—
279C2×Dic5—62no—
280C2×Dic5—61no—
281C2×Dic5—62no—
282C2×Dic5—62no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286C4×D5—68no—
287C23×C4—151no—
288#117—158no—
289C2×C4⋊C4—151no—
290C2×C4⋊C4—151no—
291C2×C4⋊C4—152no—
292C2×C4⋊C4—152no—
293C2×C4⋊C4C2×D1512yes—
294C2×C22⋊C4—151no—
295C2×C22⋊C4—151no—
296C2×C22⋊C4—152no—
297C2×C22⋊C4—152no—
298C2×C42—151no—
299C2×C42—152no—
300C2×C42—152no—
301C2×C42—152no—
302C2×C42C2×D1511yescharacteristic
303#95—151no—
304#95—151no—
305#95—152no—
306#95—152no—
307#95—152no—
308#95C2×D1511yescharacteristic
309#95C2×D1511yescharacteristic
310#95C2×D1512yes—
311C2×C3×C5C2×#11711yescharacteristic
312C2×C3×C5C4×#4111yescharacteristic
313C2×C3×C5#52011yescharacteristic
314C2×C3×C5#55212yes—
315C2×C3×C5#55512yes—
316D15—42no—
317C23×C3C23×D511yescharacteristic
318C22×D3—52no—
319C22×D3—101no—
320C22×D3—101no—
321C22×D3—102no—
322C22×D3—102no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4C2×C4×D512yes—
334C2×C3×C4C2×C4×D512yes—
335C2×C3×C4C2×C4×D512yes—
336C2×Dic3—52no—
337C2×Dic3—54no—
338C2×Dic3—52no—
339C2×Dic3—52no—
340C2×Dic3—54no—
341C2×Dic3—101no—
342C2×Dic3—101no—
343C2×Dic3—102no—
344C2×Dic3—102no—
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—102no—
348C2×Dic3—102no—
349C4×D3—108no—
350C22×C5C22×C4×D311yescharacteristic
351C22×C5#100411yescharacteristic
352C22×C5#100711yescharacteristic
353C22×C5D3×#4112yes—
354C22×C5D3×#4112yes—
355C2×D5—62no—
356C2×D5—62no—
357C2×D5—62no—
358C2×D5—122no—
359C2×D5—122no—
360C4×C5—22no—
361C4×C5—22no—
362C4×C5—22no—
363C4×C5—42no—
364C4×C5—42no—
365Dic5—34no—
366Dic5—64no—
367Dic5—62no—
368Dic5—62no—
369Dic5—122no—
370C24—151no—
371C22×C4—151no—
372C22×C4—152no—
373C22×C4—151no—
374C22×C4—151no—
375C22×C4—154no—
376C22×C4—152no—
377C22×C4—304no—
378C22×C4C22×D1512yes—
379C22×C4C22×D1512yes—
380C22×C4C22×D1511yescharacteristic
381C22×C4C22×D1511yescharacteristic
382C22×C4C22×D1511yescharacteristic
383C4⋊C4—42no—
384C4⋊C4—154no—
385C4⋊C4—154no—
386C4⋊C4—304no—
387C4⋊C4—602no—
388C22⋊C4—154no—
389C22⋊C4—154no—
390C22⋊C4—304no—
391C22⋊C4—602no—
392C42—154no—
393C42—304no—
394C42—304no—
395C42—304no—
396C42C4×D1514yes—
397C3×C5#234611yescharacteristic, complemented, Hall
398C22×C3C22×C4×D511yescharacteristic
399C22×C3#414411yescharacteristic
400C22×C3#414711yescharacteristic
401C22×C3D5×#4112yes—
402C22×C3D5×#4112yes—
403C2×D3—102no—
404C2×D3—102no—
405C2×D3—102no—
406C2×D3—202no—
407C2×D3—202no—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—42no—
412C3×C4—42no—
413Dic3—54no—
414Dic3—102no—
415Dic3—102no—
416Dic3—104no—
417Dic3—202no—
418C2×C5#550411yescharacteristic
419C2×C5D3×#11711yescharacteristic
420C2×C5#552211yescharacteristic
421C2×C5#567012yes—
422C2×C5#569312yes—
423D5—122no—
424C23—152no—
425C23—301no—
426C23—301no—
427C23—302no—
428C23—302no—
429C23C23×D1511yescharacteristic
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—152no—
441C2×C4—154no—
442C2×C4—152no—
443C2×C4—152no—
444C2×C4—154no—
445C2×C4—308no—
446C2×C4—301no—
447C2×C4—302no—
448C2×C4—301no—
449C2×C4—302no—
450C2×C4—302no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—302no—
454C2×C4C2×C4×D1512yes—
455C2×C4C2×C4×D1512yes—
456C2×C4C2×C4×D1512yes—
457C2×C3#6583811yescharacteristic
458C2×C3D5×#11711yescharacteristic
459C2×C3#6585611yescharacteristic
460C2×C3#6600412yes—
461C2×C3#6602712yes—
462D3—202no—
463C5#7415611yescharacteristic, complemented, Sylow
464C22—302no—
465C22—302no—
466C22—302no—
467C22—602no—
468C22—602no—
469C22C22×C4×D1511yescharacteristic
470C22#9209511yescharacteristic
471C22#9209811yescharacteristic
472C22#41×D1512yes—
473C22#41×D1512yes—
474C4—22no—
475C4—22no—
476C4—22no—
477C4—42no—
478C4—42no—
479C4—154no—
480C4—304no—
481C4—302no—
482C4—302no—
483C4—602no—
484C3#1060588711yescharacteristic, complemented, Sylow
485C2—602no—
486C2#1175626311yescharacteristic
487C2D15×#11711yescharacteristic
488C2#1175628111yescharacteristic
489C2#1175642912yes—
490C2#1175645212yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#382C2
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#382D15
hypocenterC3×C5#2346
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #382

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×C5×#382C2semidirect
4. #11751077C2semidirect
5. #11751033C2semidirect
9. #11750751C2semidirect
10. #11750750C2semidirect
11. #11750749C2semidirect
28. #91761C4semidirect
39. C5×#382D3semidirect
77. C3×#382D5semidirect
201. #382D15semidirect
397. C3×C5#2346semidirect
463. C5#74156semidirect
484. C3#10605887semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#917612
C3×C5×#3822
#117510912
#117510772
#117510332
#117507702
#117507682
#117507672
#117507512
#117507502
#117507492
#106058873
#741565